Lecture

Crystal Structures: Miller Indices and Lattice Planes

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

CH-450: Solid state chemistry and energy applications

You will learn about the bonding and structure of several important families of solid state materials. You will gain insight into common synthetic and characterization methods and learn about the applicability of several classes of materials in energy rele ...

Description

This lecture covers the concepts of projected views, Miller indices, lattice planes, and directions in crystal structures, including close-packed structures, interstitial sites, and the identification of Miller Indices for different planes.

Instructor

Wendy Lee Queen

Teaching & PhD PhD Students Pratap Narayan Soni, Pattaraphon Rodlamul, Matthieu Meoli, Olivier Thomas Smith, Sanjay Venkatachalam, Anne Faustine Sido Belin, Christopher William Gardner, Lorenzo Meneghin Past EPFL PhD Students Mehrdad Asgari, Daniel Teav Sun, Ilia Kochetygov, Vikram Vinayak Karve, Anita Justin, Till Marian Schertenleib, Jocelyn Richard Roth, Timo Markus Oskar Felder Courses Chemical engineering practice ChE-309 This course provides the students with practical experience wit

Official source

Related concepts (20)

Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cF or fcc) Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals.

Bragg's law

In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals.

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography.

Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.

Crystal system

In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.

Related lectures (64)

Supramolecular Organisation: Solid State

Explores the supramolecular organization of π-conjugated molecules in the solid state, covering crystal structures and packing preferences.

Electron Diffraction: Basics and Applications

Covers the fundamentals of electron diffraction and its applications in understanding crystal structures and symmetry, including lattice vectors, lattice planes, and dark-field imaging techniques.

Crystal Structures: Reciprocal Lattice and Brillouin Zones

Covers crystallography concepts, including veganicide cells, reciprocal lattices, and Brillouin zones, essential for understanding electron behavior in crystal structures.

Crystal Structures: Cubic Lattices & Miller Indices

Explores cubic crystal structures, coordination numbers, and packing factors in metals and alloys.

Crystal Packing of Conjugated Molecules